2032
Ind. Eng. Chem. Res. 1996, 35, 2032-2038
Development of a Universal Group Contribution Model for Single-Component and Multicomponent Adsorption of Liquids on Various Adsorbents (UGCMA) Thorsten Friese, Peter Ulbig, and Siegfried Schulz* Lehrstuhl fu¨ r Thermodynamik, Universita¨ t Dortmund, 44227 Dortmund, Germany
A new approach to the complex topic of liquid-phase adsorption onto a solid surface is presented in this paper using group contribution models, as they are already successfully applied to the VLE and LLE. Not only are the interactions between the groups of the liquid components in the surface phase, which differ with regard to the bulk phase, taken into consideration but also the adsorption-specific interactions with the solid surface are treated now in terms of group contributions. The interaction parameters have to be fitted to experimental surface-excess data as well as to those of heats of immersion. Once well-fitted parameters are finally available, heats of immersion, surface-phase activity coefficients, and phase equilibrium can be calculated. The introduction of special parameters, which take account of the geometrical and energetical heterogeneity of the surface, offers the possibility of applying the developed model to various adsorbents. Introduction The economical design or optimization of unit operations is extremely dependent on the knowledge of data for adsorption equilibria and heats of adsorption. However, there are significant gaps between the data published in open literature and those needed in actual practice, especially since the published values are mostly measured at standard conditions (Kaul and Sweed, 1983; Ruthven, 1984). Therefore, there is a need for an efficient model in order to calculate the behavior of real usually nonideal adsorption systems. In the past years some efforts were made with respect to this point (Everett, 1993; Woodbury and Noll, 1983, 1989; Schiby and Ruckenstein, 1985; Rudzinski and Partyka, 1981; Rudzinski et al., 1982, 1983, 1987, 1990; Messow et al., 1989, 1993; Tolmachev, 1991; Jaroniec et al., 1989; Myers and Sircar, 1970). Because of the numerous effects on liquid-phase adsorption, it turns out to be a quite complex system. Therefore, simplifying assumptions have been made. However, simplifications cause a gap with regard to the description of real system behavior. Since the modeling of the liquid-phase adsorption is not trivial, one has to take account of all accessible experimental information. Besides the surface excess nei , i.e. the preferred adsorption of a component i of a binary mixture at the considered initial concentration ad and of the xb,o i , heats of immersion of the mixture h ad,o pure component hi can be measured, as well as the temperature dependence of these quantities. It was the aim of our work to develop a liquid-phase adsorption model on the basis of group contributions and to present the possibilities of obtaining well-fitted parameters, in order to allow the prediction of nonideal surface-phase behavior and heats of immersion. Theory The starting point of the development is the application of the classical thermodynamic VLE formulation to the adsorption equilibrium of a liquid component i in the bulk phase b and in the adsorbed surface phase s. According to Kaul and Sweed (1983), it is S0888-5885(95)00596-3 CCC: $12.00
γbi xbi pSi
{
f bi ) f si
}
(1)
{
}
(p - pSi )vi gad,o - gad i s s S exp ) γi xi pi exp RT RTnsi /m
(2)
The left-hand side of eq 2 is the well-known description of a nonideal liquid bulk phase. The integral of the Poynting term exp(∫ppSi (vi/RT)dp) is solved by assuming a pressure-independent molar volume vi. The bulk phase is in equilibrium with the adsorbed surface phase, whose properties, however, are influenced by the solid adsorbent. The real behavior of the surface phase can also be described by an activity coefficient γsi (right-hand side of eq 2). γsi is a function of the surface-phase composition xsi . The influence of the solid surface is taken into account by the change of the molar Gibbs enthalpy of adsorption with regard to the pure component gad,o - gad. i The activity coefficient γbi (xbi ) and the saturation pressure pSi in the bulk phase can be calculated straightforward by using appropriate models. In order to prepare an equilibrium diagram xsi ) f(xbi ) from eq 2, there is a need of further models for predicting the surface-phase coefficient γsi (xsi ) and the Gibbs enthalpy of adsorption gad of the mixture and of the pure components gad,o , respectively. i The following chapters deal with our proposals with regard to that point. Group Contribution Modeling of the Heat of Immersion The parameters of a heat of immersion model must be fitted to experimental had data. We want to describe the heat of immersion by modifying existing group contribution models, e.g., UNIFAC (Fredenslund et al., 1975) or EBGCM (Ulbig et al., 1996b). First of all, we consider the adsorption of a pure component: The solid adsorbent and the pure liquid substance form a two-component mixture. If these two components get into contact, a “heat of mixing” occurs, called the heat of immersion had,o. The EBGC model, © 1996 American Chemical Society
Ind. Eng. Chem. Res., Vol. 35, No. 6, 1996 2033
predict the measured heat of immersion within the range 0 < x*s e xss,*. The only permissible point with regard to the applicability of an existing group contribution model is at the saturation concentration xss,*, s,* because only at this point does xs,* i + xs ) 1 apply; i.e., the pseudo molar fraction of the pure liquid can be calculated. This corresponds to the idea that the heat effect is based on a certain number of liquid molecules, related to the extent of the solid surface, and each additional liquid molecule can be neglected. Nevertheless, all the experimental data taken within the range s,* 0 < x* s e xs can be used to fit the interaction parameters of the had,*(xss,*) model. So, the pseudosystem consists of nsi moles of surfacephase liquid and of nss,* moles of solid adsorbent, and therefore
Figure 1. Illustration of the pseudo heat of mixing.
for instance, allows the calculation of the excess enthalpy hE, occurring in a nonideal liquid mixture in units of joules per mole of mixture. In the adsorption model the heat had,* can be looked upon as an analogous quantity considering the pseudomixture of the pure liquid with the solid (symbolized by the asterisk). However, the measured heat of immersion has the units joules per gram of adsorbent. The modeling of this quantity had,o requires the correlation using a pseudo molar fraction xss,*[mols/molmix] and a pseudo molar mass M* s [gs/mols] of the solid:
xs,*s
ns,*s )
(6)
ns,*s + nsi
Equation 5 yields the number of solid moles nss,*. The number of liquid moles results from the assumption of a multilayer model: The molar space requirement wi of the liquid component i can be estimated according to Young (1968):
wi ) 21/3NA(vi/NA)2/3
(7)
Assuming t layers in the multilayer model, it is: ,
s, had o ) had,*/M* sx * s
(3)
The model for had,* contains the solid-liquid interaction parameters, which can be fitted to experimental data when using eq 3. The pseudo molar mass results from the assumption that the total surface of the adsorbent As ) masp corresponds to nss,* moles of a pseudo solid group, having the mole-specific group surface Q of an arbitrarily chosen reference group, e.g., the aromatic carbon group aC
masp ) ns,* s QaC
(4)
with QaC ) 30 000 m2/mol according to van der Waals. Thus, if the specific surface asp of the adsorbent is known, its pseudo molar weight can be calculated
M* s )
QaC m ) s, asp n * s
(5)
Ast aspmt ) wi wi
w xs,*s )
(8)
1 QaC
(9)
t 1 + QaC wi
According to Tolmachev (1991), the number of layers should be correlated to the system pressure, e.g., at ambient pressure po 90% of tmax layers are assumed to be filled: t ) tmax[1 - 0.1 exp(-(p/p0 - 1))]. Assuming the existence of a surface phase in order to describe liquid phase adsorption behavior leads inevitably to the lack of knowledge about its extension. So, at last the maximum number of layers tmax has to be chosen arbitrarily but should be equal to less than 4. had,*(xss,*) is calculated from the modified group contribution model containing the parameters of the solidliquid group interactions. Before going into details, we shall extend the applicability of the had model to the immersion of the solid in a binary liquid mixture. The heat is then composed of the following parts:
had )
1 (had,*(xs,*s,xs,*i ) s, M* s x * s
E b (1 - xs,*s)hE(xsi ) + (1 - xs,*s)(hE(xb,o i ) - h (xi )) (10)
}
Before considering the composition xss,* in detail, we shall illustrate the relation between the absolute values of the heats had,* and had,o, respectively, and the molar fraction x* s of the pseudomixture by means of Figure 1. If adsorbent is given into a definite amount of a pure liquid, the experimental heat of immersion rises immediately from zero to a definite value had,o. Since it is a mass specific heat, it will remain constant by further increase of x* s. Once the concentration exceeds saturas,* tion x* s > xs there are not enough liquid molecules left to form a complete surface phase or even to cover the solid surface completely. In that case the heat of immersion decreases and finally becomes zero at the state of pure solid x*s)1. The behavior of the pseudo heat of mixing had,*(x*s) follows from eq 3. Therefore, one point of the straight line starting from the origin must be known in order to
nsi )
∆hb The pseudoheat had,*(xss,*,xs,* i ) occurs when “mixing” the three components, two liquids, and one solid. hE(xsi ) is the classical excess enthalpy of a liquid mixture at surface-phase composition xsi . Due to the surface excess during the adsorption, the bulk-phase composition will change and cause a heat contribution ∆hb.
2034
Ind. Eng. Chem. Res., Vol. 35, No. 6, 1996
If the compositions of the liquid phases considered are known, the excess enthalpies hE can be calculated, e.g., by use of EBGCM parameters. The initial bulk-phase concentrations xb,o i and those at adsorption equilibrium xbi have to be measured. The knowledge of the mass of adsorbent m and the total number of liquid moles no allows the calculation of the surface excess (Everett, 1993):
nei )
no b,o (x - xbi ) m i
(11)
The application of the multilayer model proposed by Messow et al. (1992) yields the composition of the liquid surface phase xsi as a function of xbi :
aspt b x + ne2 w1 2 s b x2(x2) ) aspt w2 e + 1n w1 w1 2
(
)
(12)
(13)
From that the mean molar space requirement w j follows
w j ) 21/3NA
( ) vj
2/3
NA
(14)
and finally the total number of liquid moles ns1 + ns2 within the surface phase
ns1 + ns2 ) aspmt/w j
(15)
The number of solid moles nss can be calculated as shown above. Thus, the pseudocomposition reads: s,
x * s )
xs,* i )
nss nss + ns1 + ns2 (ns1 + ns2)xsi nss + ns1 + ns2
(16)
(17)
Now the modified EBGC model had,* can be applied to mixtures as well as to pure components. The original EBGCM by Ulbig et al. (1996b) reads (see the appendix for more details): E hEBGCM )
(i) ν(i) ∑i xi∑ m (m - m ) m
(18)
Equation 18 modified with regard to the adsorption yields (1) (2) (2) s, ν(1) ∑ m (m - m ) + x * 2∑νm (m - m ) + m m (s) xs,* s∑νm m (19) m
had,* ) xs,* 1
respectively considering the pure component
(20)
A pseudo solid molecule containing ν(s) m fractions of pseudogroups m is assumed. The groups of the liquid phase interact with these solid groups as well as among each other. Within the solid, there are no interactions between the solid groups, i.e., (s) s ) 0. The interactions between liquid groups of different main groups can be described using the six already fitted parameters hij, aij1, aij2, hji, aji1, and aji2 of EBGCM. The parameters of the solid-liquid interaction take into account the adsorption-specific properties. According to Sircar (1986), the heat of immersion only varies slightly with regard to temperature. Therefore, we cancel the extended temperature dependence of EBGCM, described by aji2, i.e., ais2 ) asi2 ) 0. Up to this point, only four parameters per solid-liquid main-group interaction remain. Adsorbent-Specific Parameters
For had,* one needs to know the composition of the pseudo three-component mixture (xss,*,xs,* i ). For that purpose a mean molar volume vj of the two liquids must be calculated first
vj ) xs1v1 + xs2v2
(1) (s) s, ν(1) ∑ m (m - m ) + x * s∑νm m m m
had,* ) xs,*1
Apart from the specific surface area, all the other solid-specific properties which affect the heat of immersion have to be taken into consideration by the solidliquid group interaction parameters. As a matter of fact, different adsorbents with the same specific surface usually vary in their heats of immersion, although they are immersed by the same liquid. The variations occur not only between adsorbents of different classes, e.g., active carbons and zeolites, but also between two carbons, for instance, which were activated in different ways. This effect is due to both the texture of the surface, i.e., the pore size and the pore size distribution, and the energetical heterogeneity of the surface, i.e., the polarity. A quintessence of the correlations documented in the literature (Bikerman, 1958; Clint et al., 1969; Findenegg and Everett, 1969; Kazmierczak et al., 1991; Matayo and Wightman, 1973; Melkus et al., 1987; Messow et al., 1990; Tsutsumi et al., 1993; Widyani and Wightman, 1982), supplemented by our own results, can be summarized as follows: 1. A polar surface has an increasing influence with regard to the heat of immersion the smaller and the more polar the liquid molecules are. 2. The heat contribution of large nonpolar molecules is influenced rather by the geometric surface structure than by its polarity. 3. An increasing chain length of the molecules, on the one hand, leads to a decrease of the heat of immersion at porous adsorbents, since small pores become inaccessible and, on the other hand leads to an increase of the heat of immersion at nonporous surfaces, due to the orientation effect of molecules within higher layers. Consideration of the Surface Polarity Suitable methods are available in order to determine the kind and number of different functional groups at the surface of the adsorbent (Jankowska et al., 1991). Although one should think that the great variety of solid-liquid group interactions would take into account the complexity of the adsorption phenomena, there are some shortcomings in this consideration: The information needed on the adsorbent properties is often unknown. Therefore, the application of the model requires extensive experimental examinations in
Ind. Eng. Chem. Res., Vol. 35, No. 6, 1996 2035
order to predict surface-phase behavior. Furthermore, for each different solid-liquid interaction there are four parameters to be fitted. Already a few different surface groups lead to a nonproportional increase of adorptionspecific parameters with regard to the amount of data needed for the fitting procedure. Since experimental data of adsorption properties published in the literature hardly ever include any information about surface functional groups, these data cannot be used for fitting the parameters. In order to overcome these difficulties, only three functional groups at the solid surface are taken into account, nonpolar and positively and negatively charged ones, and thus the number of parameters per solidliquid interaction is restricted to 12. The three pseudogroups divide the accessible surface area into two polar regions and a nonpolar one, whose sizes vary according to the adsorbent, with (s) (s) (s) νpolar + νpolar + νnonpolar )1 + -
(21)
These fractions have to be correlated to polarity-specific properties of the adsorbent, e.g., its pH value, which, on the one hand, can be measured by simple methods (Jankowska et al., 1991) and, on the other hand, is partly available in the literature and the amounts of charged surface groups, respectively. Consideration of the Surface Geometry Furthermore, the influence of the geometric heterogeneity of the surface mentioned above should be correlated to an easily obtainable adsorbent quantity, too. In this context geometric heterogeneity means the accessibility of the specific surface. Up to this point its extension is linear correlated to the heat of immersion by using the pseudo molar weight M*s. The specific surface can be calculated by different methods. Applying the BET method, surface areas are detected by the nitrogen molecules within the porous structure of the solid, which are inaccessible to greater liquid molecules; i.e., a porous and a nonporous surface of the same adsorbent, immersed by the same liquid, show different heats, although the BET surfaces are equal. The porosity can be classified by the additional calculation of the specific surface using another method, e.g., the iodine adsorption. According to Jankowska et al. (1991), the study of the process of iodine adsorption is a simple and quick test for estimating the specific I surface area, e.g., of active carbon. The area asp calculated by this method is lower than that by BET if the proportion of pores smaller than 1 nm is significant. N2 is assigned to a pore size in the The BET surface asp units of the nitrogen molecule (about 0.5 nm). The considered liquid molecule i can be characterized by a specific length Li calculated as the geometric mean value of its three-dimensional extensions. The correlated surface asp,i follows by interpolation. Liquid molecules, whose specific lengths are in the range 1 nm < Li < 1.5 nm, can be distinguished, furthermore, by another reference substance, e.g., methylene blue. The assigned surface can now be interpoI MB - asp . Beyond 1.5 nm asp,i is lated in the range of asp MB ) const. assumed to be constant, asp,i ) asp
With regard to the adsorption of binary liquid mixtures, the specific surface asp has to be weighted by the molar fractions of the surface phase xsi :
asp ) xs1asp,1 + xs2asp,2
(22)
Equations 12 and 22 yield an equation of second degree, which has only one solution within the interval 0 e xs2 e 1. Calculation of the Gibbs Enthalpy of Adsorption Consequently, these simplifying assumptions allow the fitting of had,* interaction parameters to heats occurring by the immersion of a solid surface, whose portion of nonpolar and polar groups and specific area are known, with the latter determined at least by two different methods. However, for the calculation of the phase equilibrium from eq 2, the molar Gibbs enthalpy of adsorption gad is needed. It follows from had by the Gibbs-Helmholtz relation and reads
gad )
1 (gad,*(xs,*s,xs,*i ) - (1 - xs,*s )gE(xsi ) + s,* M* x s s E b s (1 - xs,*s )(gE(xb,o i ) - g (xi )) + RTI(x )) (23)
with (1) ν(1) ∑ m (ln Γm - ln Γm ) + m (2) (s) s, s, x *2∑νm (ln Γm - ln Γ(2) m) + x * s∑νm ln Γm) m m
gad,* ) RT(xs,*1
(24)
(i) ν(i) ∑i xsi ∑ m (ln Γm - ln Γm ) m
(25)
(i) ν(i) ∑i xbi ∑ m (ln Γm - ln Γm ) m
(26)
gE(xsi ) ) RT gE(xbi ) ) RT
See the appendix for more details. The integration “constant” I(xs) is independent of temperature. It corresponds to a combinatorial part resulting from the formation of the surface phase and can be estimated by the entropy of solidification of the pure component or the entropy of fusion with negative sign, respectively. According to Reid et al. (1987), a further estimation of the entropy of fusion itself leads to ∆Hm,i ≈ 0.3∆Hv,i. The enthalpy of vaporization ∆Hv,i can now be calculated, e.g., by using the efficient group contribution model UNIVAP (Ulbig et al., 1994, 1996a). So, it follows:
I(xs) )
∑i xsi
-0.3∆Hv,i(Tv,i) Tm,i
(27)
Finally, all quantities needed for the calculation of the activity coefficient γsi (xsi ) from eq 2 are known. These values calculated from different experimental conditions serve as “measured data” input to fit parameters of a current γi model, e.g., UNIFAC, regarding the surface-phase composition.
2036
Ind. Eng. Chem. Res., Vol. 35, No. 6, 1996
Afterall, if all parameters are fitted, the models can be used to predict the molar fraction xsi by iteration.
ν ) number of groups Θ ) surface fraction of a group Superscripts
Conclusion A new group contribution model is presented in this paper for the liquid phase adsorption of pure liquids and binary mixtures onto a solid surface. The interaction parameters have to be fitted to heats of immersion of pure components and to surface excess data at different temperatures. The heats of immersion of mixtures may be used complementarily. Using group contributions allows the application of the model to various adsorbents, if some solid-specific quantities, such as polarity and accessibility of the surface, were determined previously by simple experiments. If all neccessary parameters are known, the heat of immersion, the surface-phase activity coefficient, and finally the surface-phase composition can be calculated by iteration. Since the number of layers of the multilayer model is correlated with the system pressure, an extension of the model to gas-phase adsorption is conceivable. At the moment we are measuring heats of immersion of pure liquids on active carbon in order to extend the data base for the fitting procedure of the solid-liquid interaction parameters. The liquid-liquid interaction parameters of EBGCM are already available. The next step is the measuring and the implementation of surface excess data. Thus, γsi parameters can be fitted, and the efficiency of the model in order to predict the surface-phase composition can be proved.
ad ) adsorption ad,o ) adsorption of the pure component b ) bulk-phase b,o ) bulk-phase initial conditions e ) excess quantity E ) excess quantity (i) ) molecule component (s) ) solid component s ) surface phase S ) saturation conditions Subscripts aC ) aromatic carbon subgroup i ) component m ) group s ) solid component or group
Appendix The group excess enthalpic factor m of group m in the mixture, respectively that within the pure component i, (i) m , of the original EBGCM is given by
{
m )
Qm
Nomenclature ajm1, ajm2 ) interaction parameter between groups j and m asp ) mass-specific accessible surface A ) accessible surface f ) fugacity g ) molar Gibbs enthalpy h ) molar enthalpy hjm ) interaction parameter between groups j and m ∆Hm ) enthalpy of melting ∆Hv ) enthalpy of vaporization I(xs) ) integration “constant” depending on mole fraction L ) characteristical molecule length m ) mass of adsorbent M ) molar mass n ) number of moles NA ) Avogadro’s constant p ) pressure Q ) relative van der Waals group surface R ) universal gas constant t ) number of layers in the multilayer model T ) absolute temperature Tm ) absolute temperature of melting Tv ) absolute temperature of vaporization T0 ) reference temperature (298.15 K) v ) molar volume w ) molar space requirement x ) mole fraction
hjm
∑j Θja
[
hkj amj1 + amj2(T - T0) Θk akj1 k ΘpGpj K*J
∑
ΘjGmj
∑p
1
∑p
(
{
Qm
∑j
Θ(i) j
J*M
∑j
hjm
ΘpGpj)2
1
(28)
+ apm2(T - T0)) +
ajm1
Θ(i) j Gmj
∑k
K*J
Θ(i) k
∑p
[
Θ(i) p Gpm
hkj amj1 + amj2(T - T0)
akj1
-
∑p
∑p Θ(i)p Gpj(apj
1
( with
]}
+ apj2(T - T0))
∑p Θ(i)p Gpm(apm
Greek Letters ) group excess enthalpic factor γ ) activity coefficient Γ ) activity coefficient of a group
+ apm2(T - T0))
∑p ΘpGpm
∑p ΘpGpj(apj (i) m )
1
+
jm1
J*M
∑j
∑p ΘpGpm(apm
∑p
Θ(i) p Gpj
]}
+ apj2(T - T0))
2 Θ(i) p Gpj)
(29)
Ind. Eng. Chem. Res., Vol. 35, No. 6, 1996 2037
QjXj
Θj )
Θ(i) j
(30)
∑p QpXp QjX(i) j
(31)
)
∑p
QpX(i) p
∑i ν(i)j xi
Xj )
(32)
∑p ∑i
ν(i) p xi
ν(i) j
X(i) j
(
Gkj ) exp -
(33)
)
∑p
ν(i) p
)
akj1 + akj2(T ln(T0/T) + T - T0) RT
(34)
The considered subgroups (e.g., k and j) belong to different main groups (symbolized by the notation K * J). From this, the activity coefficients of group m in the mixture and in the pure component can be calculated by applying the Gibbs-Helmholtz equation:
(
ln Γm ) Qm
hkj
∑j Θj ∑k Θka K*J
(
(
ln Γ(i) m ) Qm
∑p
kj1
∑j Θja
J*M
ΘpGpm) -
∑j ∑k ∑p ΘpGpjK*J
K*J
∑p
Θ(i) p Gpm)
hjm
-
kj1
∑j Θja
J*M
Θ(i) j Gmj
-
ln
jm1
ΘjGmj
hkj
∑j Θ(i)j ∑k Θka
ln(
hjm
-
)
hkj Θk (35) akj1
×
jm1
hkj
∑j ∑k Θka (i) Θ G ∑p p pjK*J kj
1
)
(36)
The index variables of the sums refer to all subgroups of the system; i.e., within the pseudosystem of adsorption the solid groups are included. Literature Cited Bikerman, J. J. Surface Chemistry, Theory and Applications; Academic Press Inc.: New York, 1958. Clint, J. H.; Clunie, J. S.; Goodman, J. F.; Tate, J. R. Heats of immersion of “Graphon” in homologous series of n-Alkanes and n-Alkanols. Nature 1969, 223, 51. Everett, D. H. Thermodynamics of interfaces: An appreciation of the work of Geza Schay. Colloids Surfaces 1993, 71, 205-217. Findenegg, G. H.; Everett, D. H. Calorimetric evidence for the structure of films adsorbed at the solid/liquid interface: The
heats of wetting of “Graphon” by some n-Alkanes. Nature 1969, 223, 52. Fredenslund, A.; Jones, R. L.; Prausnitz, J. M. Group-contribution estimation of activity coefficients in nonideal liquid mixtures. AIChE J. 1975, 21, 1086-1099. Jankowska, H.; Swiatkowski, A.; Choma, J.; Kemp, T. J. Active Carbon; Ellis Horwood Ltd.: Chichester, U.K., 1991. Jaroniec, M.; Madey, R.; Dabrowski, A. Assessment of microporosity in porous adsorbents by comparing the liquid-solid adsorption isotherms. Langmuir 1989, 5, 987-990. Kaul, B. K.; Sweed, N. H. In Adsorption equilibrium data and model needs. Fundamentals of adsorption. Proceedings of the engineering foundation conference; Myers, A. L., Ed.; Schloss Elman: Germany, 1983. Kazmierczak, J.; Biniak, S.; Swiatkowski, A.; Radeke, K.-H. Interdependence of different parameters characterizing the chemistry of an activated carbon surface. J. Chem. Soc., Faraday Trans. 1991, 87 (21), 3557-3561. Matayo, D. R.; Wightman, J. P. Isotherms and enthalpies of immersion for adsorption on silica and carbon from binary solutions of Benzene, Cyclohexane and Ethyl Alcohol. J. Colloid Interface Sci. 1973, 44 (1), 162. Melkus, T. G.; Chiang, S. H.; Wen, W. W. An experimental study of heat of immersion of coal. Colloids Surf. 1987, 28, 109-121. Messow, U.; Heuchel, M.; Bra¨uer, P.; Jaroniec, M. Phenomenologigal thermodynamics of adsorption from binary non-electrolytic liquid mixtures on solid surfaces. Chem. Scr. 1989, 29, 353360. Messow, U.; Herden, H.; Bra¨uer, P.; Heuchel, M.; Pysz, M. Adsorptive Charakterisierung der Aktivkohlen R23, WRK1 und AS aus der Gas- und aus der Flu¨ssigphase. Chem. Tech. 1990, 42, 6. Messow, U.; Bra¨uer, P.; Heuchel, M.; Pysz, M. Zur experimentellen U ˆ berpru¨fung der Vorhersage von Gleichgewichtsdiagrammen bei der Adsorption bina¨rer flu¨ssiger Mischungen in poro¨sen Festko¨rpern. Chem. Tech. 1992, 44, 56-59. Messow, U.; Heuchel, M.; Bra¨uer, P.; Kind, T.; von Szombathely, M.; Jaroniec, M. Mathematische und numerische Probleme bei der thermodynamischen Auswertung von Exzeisothermen fu¨r die Adsorption bina¨rer flu¨ssiger Mischungen an Festko¨rpern. Chem. Tech. 1993, 45 (1), 2-12. Myers, A. L.; Sircar, S. Statistical thermodynamics of adsorption from liquid mixtures on solids. J. Phys. Chem. 1970, 74 (14), 2828. Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids; McGraw-Hill Book Co.: New York, 1987; p 232. Rudzinski, W.; Partyka, S. Adsorption from solutions on solid surfaces. J. Chem. Soc., Faraday Trans. 1 1981, 77, 2577-2584. Rudzinski, W.; Narkiewicz-Michalek, J.; Partyka, S. Adsorption from solutions onto solid surfaces. J. Chem. Soc., Faraday Trans. 1 1982, 78, 2361-2368. Rudzinski, W.; Michalek, J.; Zajac, J.; Partyka, P. Excess isotherms and heats of immersion in monolayer adsorption from binary liquid mixtures on slightly heterogeneous solid surfaces. Fundamentals of adsorption. In Proceedings of the engineering foundation conference; Myers, A. L., Ed.; Engineering Foundation: New York, 1983. Rudzinski, W.; Zajac, J.; Wolfram, E.; Paszli, I. Heats of immersion in multilayer adsorption from binary liquid mixtures on strongly heterogeneous solid surfaces. Colloids Surf. 1987, 22, 317-336. Rudzinski, W.; Michalek, J.; Zajac, J. Adsorption from binary liquid mixtures onto graphites: Effects of the residual heterogeneity of graphites on the excess isotherms and heats of immersion. Langmuir 1990, 6, 1505-1511. Ruthven, D. M. Principles of adsorption and adsorption processes; John Wiley & Sons Inc.: New York, 1984. Schiby, D.; Ruckenstein, E. Adsorption from multicomponent mixtures: Effect of the size of the molecules on adsorption isotherms. Colloids Surf. 1985, 15, 17-33. Sircar, S. Thermodynamics of adsorption from binary liquid mixtures on heterogeneous adsorbents. J. Chem. Soc., Faraday Trans. 1986, 1 (82), 831-841. Tolmachev, A. M. Thermodynamic theory of stoichiometric adsorption. Langmuir 1991, 7, 1400-1408. Tsutsumi, K.; Matsushima, Y.; Matsumoto, A. Surface heterogeneity of modified active carbons. Langmuir 1993, 9, 2665-2669. Woodbury, G. W.; Noll, L. A. Heat of adsorption of liquid mixtures on solid surfaces: Comparison of theory and experiment. Colloids Surf. 1983, 8, 1-15.
2038
Ind. Eng. Chem. Res., Vol. 35, No. 6, 1996
Woodbury, G. W.; Noll, L. A. Adsorption of a three-component solution onto a solid. Colloids Surf. 1989, 40, 9-30. Ulbig, P.; Schulz, S.; Klu¨ppel, M. UNIVAPsA Group Contribution Method for the Prediction of Enthalpies of Vaporization of Pure Substances. Fluid Phase Equilib. 1994, 1-15. Ulbig, P.; Schulz, S.; Klu¨ppel, M. Extension of the UNIVAP group contribution method: Enthalpies of vaporization of special alcohols in the temperature range from 313 to 358 K. Thermochim. Acta 1996a, in press. Ulbig, P.; Friese, T.; Schulz, S.; Bosch, C. Development of an Enthalpy Based Group Contribution gE-Model (EBGCM) Part 1: Activity Coefficients at Infinite Dilution. Fluid Phase Equilibr. 1996b, in press. Widyani, E.; Wightman, J. P. Thermodynamics and kinetics of immersion of coal by n-alcohols. Colloids Surf. 1982, 4, 209212.
Young, C. L. Activity Coefficients of Solutions of C4-C8 Hydrocarbons in n-Tetracosane and n-Dotriacontane. Trans. Faraday Soc. 1968, 64, 1537-1546.
Received for review September 26, 1995 Revised manuscript received January 31, 1996 Accepted February 6, 1996X IE950596C
X Abstract published in Advance ACS Abstracts, April 1, 1996.
